Question

graph the line with the equation $y = -x + 6$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = -x + 6 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=- 1\) and \( b = 6 \). The y - intercept is the point where the line crosses the y - axis, so the point is \( (0,6) \) (already plotted on the graph).

Step2: Use the slope to find another point

The slope \( m=-1=\frac{\text{rise}}{\text{run}}=\frac{- 1}{1} \). Starting from the point \( (0,6) \), we can move down 1 unit (because the rise is - 1) and then 1 unit to the right (because the run is 1). So we get the point \( (0 + 1,6-1)=(1,5) \). We can also move up 1 unit and 1 unit to the left (since \( \frac{1}{-1} \) is also equal to - 1), starting from \( (0,6) \), we get the point \( (0 - 1,6 + 1)=(-1,7) \).

Step3: Draw the line

Now that we have two or more points (e.g., \( (0,6) \), \( (1,5) \), \( (-1,7) \)), we can draw a straight line passing through these points.

To graph the line:

1. Start at the y - intercept \( (0,6) \).
2. Use the slope \( - 1 \) to find additional points. For example, from \( (0,6) \), moving 1 unit right and 1 unit down gives \( (1,5) \); moving 1 unit left and 1 unit up gives \( (-1,7) \).
3. Draw a straight line through these points.

The line should pass through all the points that satisfy the equation \( y=-x + 6 \).

(Note: Since the question is about graphing, the final answer is the graph of the line \( y=-x + 6 \) passing through points like \( (0,6) \), \( (1,5) \), \( (-1,7) \) etc. )

Answer:

Step1: Identify the slope and y-intercept

The equation \( y = -x + 6 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=- 1\) and \( b = 6 \). The y - intercept is the point where the line crosses the y - axis, so the point is \( (0,6) \) (already plotted on the graph).

Step2: Use the slope to find another point

The slope \( m=-1=\frac{\text{rise}}{\text{run}}=\frac{- 1}{1} \). Starting from the point \( (0,6) \), we can move down 1 unit (because the rise is - 1) and then 1 unit to the right (because the run is 1). So we get the point \( (0 + 1,6-1)=(1,5) \). We can also move up 1 unit and 1 unit to the left (since \( \frac{1}{-1} \) is also equal to - 1), starting from \( (0,6) \), we get the point \( (0 - 1,6 + 1)=(-1,7) \).

Step3: Draw the line

Now that we have two or more points (e.g., \( (0,6) \), \( (1,5) \), \( (-1,7) \)), we can draw a straight line passing through these points.

To graph the line:

1. Start at the y - intercept \( (0,6) \).
2. Use the slope \( - 1 \) to find additional points. For example, from \( (0,6) \), moving 1 unit right and 1 unit down gives \( (1,5) \); moving 1 unit left and 1 unit up gives \( (-1,7) \).
3. Draw a straight line through these points.

The line should pass through all the points that satisfy the equation \( y=-x + 6 \).

(Note: Since the question is about graphing, the final answer is the graph of the line \( y=-x + 6 \) passing through points like \( (0,6) \), \( (1,5) \), \( (-1,7) \) etc. )